An efficient renovation on kernel Fisher discriminant analysis and face recognition experiments

A reformative kernel algorithm, which can deal with two-class problems as well as those with more than two classes, on Fisher discriminant analysis is proposed. In the novel algorithm the supposition that in feature space discriminant vector can be approximated by some linear combination of a part of training samples, called “significant nodes”, is made. If the “significant nodes” are found out, the novel algorithm on kernel Fisher discriminant analysis will be superior to the naive one in classification efficiency. In this paper, a recursive algorithm for selecting “significant nodes”, is developed in detail. Experiments show that the novel algorithm is effective and much efficient in classifying.     

A reformative kernel Fisher discriminant analysis

A reformative kernel Fisher discriminant method is proposed, which is directly derived from the naive kernel Fisher discriminant analysis with superiority in classification efficiency. In the novel method only a part of training patterns, called “significant nodes”, are necessary to be adopted in classifying one test pattern. A recursive algorithm for selecting “significant nodes”, which is the key of the novel method, is presented in detail. The experiment on benchmarks shows that the novel method is effective and much efficient in classifying.     

鉴别分析方法的最优化问题研究

提出了一种核Fisher鉴别分析方法优化方案,并分别给出了解决两类分类和解决多于两类的分类问题的算法,该方案具有明显的分类效率上的优势。在这种方案的实现中,首先从总体训练样本中选择出“显著”训练样本,对测试样本的分类只依赖于测试样本与“显著”训练样本之间的核函数。还设计出了一种选择“显著”训练样本的递归算法,以降低算法的计算复杂度。将该算法应用于人脸图象数据库与“基准”数据集,得到了很好的实验效果。     

一种基于核的快速非线性鉴别分析方法

基于“核技巧”提出的新的非线性鉴别分析方法在最小二乘意义上与基于核的Fisher鉴别分析方法等效,相应鉴别方向通过一个线性方程组得出,计算代价较小,相应分类实现极其简便．该方法的最大优点是,对训练数据进行筛选,可使构造鉴别矢量的“显著”训练模式数大大低于总训练模式数,从而使得测试集的分类非常高效;同时,设计出专门的优化算法以加速“显著”训练模式的选取．实验表明,这种非线性方法不仅具有明显的效率上的优势,且具有不低于基于核的Fisher鉴别分析方法的性能．     

Kernel-based improved discriminant analysis and its application to face recognition

Kernel discriminant analysis (KDA) is a widely used tool in feature extraction community. However, for high-dimensional multi-class tasks such as face recognition, traditional KDA algorithms have the limitation that the Fisher criterion is nonoptimal with respect to classification rate. Moreover, they suffer from the small sample size problem. This paper presents a variant of KDA called kernel-based improved discriminant analysis (KIDA), which can effectively deal with the above two problems. In the proposed framework, origin samples are projected firstly into a feature space by an implicit nonlinear mapping. After reconstructing between-class scatter matrix in the feature space by weighted schemes, the kernel method is used to obtain a modified Fisher criterion directly related to classification error. Finally, simultaneous diagonalization technique is employed to find lower-dimensional nonlinear features with significant discriminant power. Experiments on face recognition task show that the proposed method is superior to the traditional KDA and LDA.     

基于核方法的雷达目标一维距离像识别

由于雷达目标及其所处环境的复杂性,导致不同目标之间的关系往往是非线性的.研究基于核的非线性方法,并将其应用于雷达目标一维距离像识别.核Fisher判别分析(KFDA)是一种抽取非线性特征的最有效方法之一,但它往往会面临小样本问题.针对此问题,给出一种null-KFDA方法,对距离像进行特征提取.然后,采用一种新的核非线性分类器——KNR(kernel-based nonlinear representor),对所提取的特征进行分类.对3种飞机的实测距离像进行实验,结果验证了null-KFDA的有效性.此外,与非线性支持向量机(SVM)和径向基函数神经网络(RBFNN)相比,KNR分类器具有更优的识别性能.     

Multi-class pattern classification using neural networks

Multi-class pattern classification has many applications including text document classification, speech recognition, object recognition, etc. Multi-class pattern classification using neural networks is not a trivial extension from two-class neural networks. This paper presents a comprehensive and competitive study in multi-class neural learning with focuses on issues including neural network architecture, encoding schemes, training methodology and training time complexity. Our study includes multi-class pattern classification using either a system of multiple neural networks or a single neural network, and modeling pattern classes using one-against-all, one-against-one, one-against-higher-order, and P-against-Q. We also discuss implementations of these approaches and analyze training time complexity associated with each approach. We evaluate six different neural network system architectures for multi-class pattern classification along the dimensions of imbalanced data, large number of pattern classes, large vs. small training data through experiments conducted on well-known benchmark data.     

Fast kernel Fisher discriminant analysis via approximating the kernel principal component analysis

Kernel Fisher discriminant analysis (KFDA) extracts a nonlinear feature from a sample by calculating as many kernel functions as the training samples. Thus, its computational efficiency is inversely proportional to the size of the training sample set. In this paper we propose a more approach to efficient nonlinear feature extraction, FKFDA (fast KFDA). This FKFDA consists of two parts. First, we select a portion of training samples based on two criteria produced by approximating the kernel principal component analysis (AKPCA) in the kernel feature space. Then, referring to the selected training samples as nodes, we formulate FKFDA to improve the efficiency of nonlinear feature extraction. In FKFDA, the discriminant vectors are expressed as linear combinations of nodes in the kernel feature space, and the extraction of a feature from a sample only requires calculating as many kernel functions as the nodes. Therefore, the proposed FKFDA has a much faster feature extraction procedure compared with the naive kernel-based methods. Experimental results on face recognition and benchmark datasets classification suggest that the proposed FKFDA can generate well classified features.     

Semi-supervised multi-class Adaboost by exploiting unlabeled data

Semi-supervised learning has attracted much attention in pattern recognition and machine learning. Most semi-supervised learning algorithms are proposed for binary classification, and then extended to multi-class cases by using approaches such as one-against-the-rest. In this work, we propose a semi-supervised learning method by using the multi-class boosting, which can directly classify the multi-class data and achieve high classification accuracy by exploiting the unlabeled data. There are two distinct features in our proposed semi-supervised learning approach: (1) handling multi-class cases directly without reducing them to multiple two-class problems, and (2) the classification accuracy of each base classifier requiring only at least 1/K or better than 1/K (K is the number of classes). Experimental results show that the proposed method is effective based on the testing of 21 UCI benchmark data sets.     

Fuzzy discriminant analysis with kernel methods

A novel fuzzy nonlinear classifier, called kernel fuzzy discriminant analysis (KFDA), is proposed to deal with linear non-separable problem. With kernel methods KFDA can perform efficient classification in kernel feature space. Through some nonlinear mapping the input data can be mapped implicitly into a high-dimensional kernel feature space where nonlinear pattern now appears linear. Different from fuzzy discriminant analysis (FDA) which is based on Euclidean distance, KFDA uses kernel-induced distance. Theoretical analysis and experimental results show that the proposed classifier compares favorably with FDA.     

极速非线性判别分析网络

由于线性判别分析仅是线性方法,难以有效应对非线性问题,而对其非线性化是解决这一问题的关键途径。非线性化判别方法主要包括神经网络和核化方法。神经网络判别分析方法虽然继承了神经网络所具有的自适应、分布存储、并行处理和非线性映射等优点,但也遗传了其训练速度慢且易陷入局部最小值缺点;而核线性判别分析方法虽能获得全局最优解析解,但因受制于隐节点数目（等于样本个数）,当数据规模大时,计算成本变大。本文受随机映射启发,对神经网络判别分析方法进行极速化改造,实现了一种极速非线性判别分析方法,兼具神经网络的自适应性和全局最优解的快速性。最后在UCI真实数据集上的实验表明,极速非线性判别分析方法具有更优的分类性能。     

Multi-class pairwise linear dimensionality reduction using heteroscedastic schemes

Linear dimensionality reduction (LDR) techniques have been increasingly important in pattern recognition (PR) due to the fact that they permit a relatively simple mapping of the problem onto a lower-dimensional subspace, leading to simple and computationally efficient classification strategies. Although the field has been well developed for the two-class problem, the corresponding issues encountered when dealing with multiple classes are far from trivial. In this paper, we argue that, as opposed to the traditional LDR multi-class schemes, if we are dealing with multiple classes, it is not expedient to treat it as a multi-class problem per se. Rather, we shall show that it is better to treat it as an ensemble of Chernoff-based two-class reductions onto different subspaces, whence the overall solution is achieved by resorting to either Voting, Weighting, or to a Decision Tree strategy. The experimental results obtained on benchmark datasets demonstrate that the proposed methods are not only efficient, but that they also yield accuracies comparable to that obtained by the optimal Bayes classifier.     

Application of Kernel-Based Feature Space Transformations and Learning Methods to Phoneme Classification

This paper examines the applicability of some learning techniques to the classification of phonemes. The methods tested were artificial neural nets (ANN), support vector machines (SVM) and Gaussian mixture modeling (GMM). We compare these methods with a traditional hidden Markov phoneme model (HMM), working with the linear prediction-based cepstral coefficient features (LPCC). We also tried to combine the learners with linear/nonlinear and unsupervised/supervised feature space transformation methods such as principal component analysis (PCA), independent component analysis (ICA), linear discriminant analysis (LDA), springy discriminant analysis (SDA) and their nonlinear kernel-based counterparts. We found that the discriminative learners can attain the efficiency of HMM, and that after the transformations they can retain the same performance in spite of the severe dimension reduction. The kernel-based transformations brought only marginal improvements compared to their linear counterparts.     

基于Gabor直方图特征和MVBoost的人脸表情识别

提出采用Gabor变换与分级直方图统计相结合的方法来提取表情特征,以分层次反映局部区域内纹理变化的信息.这比仅用一维的Gabor系数具有更强的特征表示能力.借助直方图特征,还设计了向量输入、多类连续输出的弱分类器,并嵌入到多类连续AdaBoost的算法框架中,得到了向量输入、多类输出的MVBoost方法.该方法直接对特征进行多类的判决以满足多类时分类的需求,而不必训练多个二分类的AdaBoost分类器,从而使训练过程和分类过程都得到简化.     

Adaptive linear discriminant regression classification for face recognition

Linear discriminant regression classification (LDRC) was presented recently in order to boost the effectiveness of linear regression classification (LRC). LDRC aims to find a subspace for LRC where LRC can achieve a high discrimination for classification. As a discriminant analysis algorithm, however, LDRC considers an equal importance of each training sample and ignores the different contributions of these samples to learn the discriminative feature subspace for classification. Motivated by the fact that some training samples are more effectual in learning the low-dimensional feature space than other samples, in this paper, we propose an adaptive linear discriminant regression classification (ALDRC) algorithm by taking special consideration of different contributions of the training samples. Specifically, ALDRC makes use of different weights to characterize the different contributions of the training samples and utilizes such weighting information to calculate the between-class and the within-class reconstruction errors, and then ALDRC seeks to find an optimal projection matrix that can maximize the ratio of the between-class reconstruction error over the within-class reconstruction error. Extensive experiments carried out on the AR, FERET and ORL face databases demonstrate the effectiveness of the proposed method.     

Breast cancer diagnosis using genetic programming generated feature

This paper proposes a novel method for breast cancer diagnosis using the feature generated by genetic programming (GP). We developed a new feature extraction measure (modified Fisher linear discriminant analysis (MFLDA)) to overcome the limitation of Fisher criterion. GP as an evolutionary mechanism provides a training structure to generate features. A modified Fisher criterion is developed to help GP optimize features that allow pattern vectors belonging to different categories to distribute compactly and disjoint regions. First, the MFLDA is experimentally compared with some classical feature extraction methods (principal component analysis, Fisher linear discriminant analysis, alternative Fisher linear discriminant analysis). Second, the feature generated by GP based on the modified Fisher criterion is compared with the features generated by GP using Fisher criterion and an alternative Fisher criterion in terms of the classification performance. The classification is carried out by a simple classifier (minimum distance classifier). Finally, the same feature generated by GP is compared with a original feature set as the inputs to multi-layer perceptrons and support vector machine. Results demonstrate the capability of this method to transform information from high-dimensional feature space into one-dimensional space and automatically discover the relationship among data, to improve classification accuracy.     

局部Fisher判别分析算法及仿真研究*

复杂化工过程常被多种类型的故障损坏,正常的训练数据无法建立准确的操作模型。为了提高复杂化工过程中故障的检测和分类能力,传统无监督Fisher判别分析(Fisher Discriminant Analysis,FDA)算法无法在多模态故障数据中的应用,本文提出基于局部Fisher判别分析(Local Fisher Discriminant Analysis,LFDA)的故障诊断方法。首先计算训练数据的局部类内和类间离散度矩阵,寻找LFDA的投影方向;其次把训练数据和测试数据向投影向量上投影,提取特征向量;最后计算特征向量间的欧氏距离,运用KNN分类器进行分类。把提出的LFDA方法应用到Tennessee Eastman(TE)过程,监控结果表明,LFDA的效果好于FDA和核Fisher判别分析(Kernel Fisher Discriminant Analysis,KFDA),说明LFDA方法在分类及检测不同类的故障方面具有高准确性及高灵敏度的优势。     

Fingerprint classification using fast Fourier transform and nonlinear discriminant analysis

In this paper, we present a new approach for fingerprint classification based on discrete Fourier transform (DFT) and nonlinear discriminant analysis. Utilizing the DFT and directional filters, a reliable and efficient directional image is constructed from each fingerprint image, and then nonlinear discriminant analysis is applied to the constructed directional images, reducing the dimension dramatically and extracting the discriminant features. The proposed method explores the capability of DFT and directional filtering in dealing with low-quality images and the effectiveness of nonlinear feature extraction method in fingerprint classification. Experimental results demonstrates competitive performance compared with other published results.     

A complete fuzzy discriminant analysis approach for face recognition

In this paper, some studies have been made on the essence of fuzzy linear discriminant analysis (F-LDA) algorithm and fuzzy support vector machine (FSVM) classifier, respectively. As a kernel-based learning machine, FSVM is represented with the fuzzy membership function while realizing the same classification results with that of the conventional pair-wise classification. It outperforms other learning machines especially when unclassifiable regions still remain in those conventional classifiers. However, a serious drawback of FSVM is that the computation requirement increases rapidly with the increase of the number of classes and training sample size. To address this problem, an improved FSVM method that combines the advantages of FSVM and decision tree, called DT-FSVM, is proposed firstly. Furthermore, in the process of feature extraction, a reformative F-LDA algorithm based on the fuzzy k-nearest neighbors (FKNN) is implemented to achieve the distribution information of each original sample represented with fuzzy membership grade, which is incorporated into the redefinition of the scatter matrices. In particular, considering the fact that the outlier samples in the patterns may have some adverse influence on the classification result, we developed a novel F-LDA algorithm using a relaxed normalized condition in the definition of fuzzy membership function. Thus, the classification limitation from the outlier samples is effectively alleviated. Finally, by making full use of the fuzzy set theory, a complete F-LDA (CF-LDA) framework is developed by combining the reformative F-LDA (RF-LDA) feature extraction method and DT-FSVM classifier. This hybrid fuzzy algorithm is applied to the face recognition problem, extensive experimental studies conducted on the ORL and NUST603 face images databases demonstrate the effectiveness of the proposed algorithm.     

一种新的特征提取方法及其在模式识别中的应用

核典型相关分析(KCCA)是一种有监督的机器学习方法,可以有效地提取非线性特征。然而随着训练样本数目的增加,标准的KCCA方法的计算复杂度会随之增加。针对此缺点,提出一种改进的KCCA方法：首先用几何特征选择方法选择一个训练样本子集并将其映射到再生核希尔伯特空间(RKHS),然后设计了一种提升特征提取效率的算法,该算法按照对特征分类贡献的大小巧妙地选取样本的特征值,进而求出其相应的特征向量,最后将改进的KCCA与支持向量数据描述(SVDD)多分类器相结合用于分类识别。在ORL人脸图像数据库上的实验结果表明,改进的方法相对传统的KCCA方法,在不影响识别率的情况下提高了人脸识别速度,减小了系统存储量。